Search existing math (mathlas index)

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations declare readOnlyHint and idempotentHint, which align with the description. The description adds value beyond annotations by detailing the index fusion method, optional corpus_dir behavior, and the effect of source_filter/source_weights (e.g., down-weighting hurts queries targeting that source). No contradictions.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise (5 sentences) and efficiently structured: core purpose first, then usage guidance, then parameter explanations with examples. No redundant or irrelevant information.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity (5 parameters, nested objects, output schema exists), the description covers all necessary aspects: index composition, usage pattern, parameter nuances, and follow-up tool. Output schema is present so return values need not be described.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, and the description adds significant context: explains omit for corpus_dir uses prebuilt index, provides example for source_filter, and notes important behavior about source_weights. This adds meaningful meaning beyond the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states it finds existing theorems/results from the mathlas index, specifying the index composition (dense + BM25 + RRF, fused with web_added findings). It distinguishes itself from the sibling applicability_checklist by advising to use this tool first for 'does known math solve this?' and then follow up with applicability_checklist.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explicitly tells when to use: 'Use FIRST for any does known math solve this? question.' It also provides follow-up guidance (applicability_checklist). While it doesn't explicitly state when not to use, it implies the primary use case clearly.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.